Interaction between buoyancy and diffusion-driven instabilities of propagating autocatalytic reaction fronts. II. Nonlinear simulations

D’Hernoncourt, J.; Merkin, J. H.; Wit, A. De

doi:10.1063/1.3077181

Cited by 13 publications

(16 citation statements)

References 33 publications

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“…This value is still large compared to the value of 0.769, which allows the formation of extended periodic structures. The search for these structures will require lowering the Rayleigh number by reducing the gap width or using only a small angular deviation from the horizontal position as suggested in [21]. The typical dimensionless wave number of these patterns is q = 1/ √ 3, which corresponds to a dimensioned wavelength of 1.6 mm for this system.…”

Section: Summary and Discussionmentioning

confidence: 99%

Convection in stable and unstable fronts

Elliott

Vasquez

2012

Phys. Rev. E

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Density gradients across a reaction front can lead to convective fluid motion. Stable fronts require a heavier fluid on top of a lighter one to generate convective fluid motion. On the other hand, unstable fronts can be stabilized with an opposing density gradient, where the lighter fluid is on top. In this case, we can have a stable flat front without convection or a steady convective front of a given wavelength near the onset of convection. The fronts are described with the Kuramoto-Sivashinsky equation coupled to hydrodynamics governed by Darcy's law. We obtain a dispersion relation between growth rates and perturbation wave numbers in the presence of a density discontinuity accross the front. We also analyze the effects of this density change in the transition to chaos.

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Section: Summary and Discussionmentioning

confidence: 99%

Convection in stable and unstable fronts

Elliott

Vasquez

2012

Phys. Rev. E

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“…43 At the smaller values of D, the system is also diffusionally unstable, diffusional instability requiring D Ͻ D c Ӎ 0.424 for the cubic kinetics ͓Eq. ͑1͔͒.…”

Section: Upward Propagating Frontsmentioning

confidence: 99%

“…Numerical simulations of the full nonlinear problem are discussed in a following paper. 43 We find as a result of the LSA that the problem can be classified into 12 different cases depending whether the density increases or decreases across the front, whether the front is ascending or descending in the gravity field, and whether D =1, D Ͼ 1, or D Ͻ 1. In order to demonstrate this, the present article is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Interaction between buoyancy and diffusion-driven instabilities of propagating autocatalytic reaction fronts. I. Linear stability analysis

D’Hernoncourt

Merkin

Wit

2009

The Journal of Chemical Physics

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The interaction between buoyancy-driven and diffusion-driven instabilities that can develop along a propagating reaction front is discussed for a system based on an autocatalytic reaction. Twelve different cases are possible depending on whether the front is ascending or descending in the gravity field, whether the reactant is heavier or lighter than the products, and whether the reactant diffuses faster, slower, or at the same rate as the product. A linear stability analysis ͑LSA͒ is undertaken, in which dispersion curves ͑plots of the growth rate against wave number k͒ are derived for representative cases as well as an asymptotic analysis for small wave numbers. The results from the LSA indicate that, when the initial reactant is denser than the reaction products, upward propagating fronts remain unstable with the diffusion-driven instability enhancing this instability. Buoyantly stable downward propagating fronts become unstable when the system is also diffusionally unstable. When the initial reactant is lighter than the reaction products, any diffusionally unstable upward propagating front is stabilized by small buoyancy effects. A diffusional instability enhances the buoyant instability of a downward propagating front with there being a very strong interaction between these effects in this case.

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“…For example, reaction fronts with chemicals having different diffusivities present instabilities that can be described with a KS equation [14,15]. In these reactions, front propagation coupled to convective fluid flow leads to complex behavior [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Stability of fronts in the Kuramoto-Sivashinsky equation advected by a Poiseuille flow

Vilela

Vasquez

2012

Phys. Rev. E

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We study reaction fronts described by the Kuramoto-Sivashinsky equation subject to a Poiseuille flow. The fronts propagate with or against the flow located inside a two-dimensional slab. Steady front profiles can be flat, axisymmetric, or nonaxisymmetric, depending on the gap between the plates and the average flow speed. We first obtain the steady front solutions, later executing a linear stability analysis to determine the stability of the fronts. Applying fluid flow can turn initially unstable fronts into stable fronts. Stable steady fronts propagating in the adverse direction of the Poiseuille flow are axisymmetric for slow fluid flows. However, for higher speeds an adverse flow can lead to stable nonaxisymmetric fronts. We also show regions of bistability where stable nonaxisymmetric and axisymmetric fronts can coexist.

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Interaction between buoyancy and diffusion-driven instabilities of propagating autocatalytic reaction fronts. II. Nonlinear simulations

Cited by 13 publications

References 33 publications

Convection in stable and unstable fronts

Convection in stable and unstable fronts

Interaction between buoyancy and diffusion-driven instabilities of propagating autocatalytic reaction fronts. I. Linear stability analysis

Stability of fronts in the Kuramoto-Sivashinsky equation advected by a Poiseuille flow

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